Residual migration with vertical velocity gradient

Since Stolt residual prestack migration is based on the assumption of constant velocity, we will evaluate the accuracy for velocity models having depth dependence.

We create our second synthetic model using the same reflector geometry as the previous section and using a realistic depth velocity model of v_0p=1700 m/s with a gradient of 0.15 s^-1 and v_0s=300 m/s with a gradient of 0.35 s^-1,

 

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Figure 5 Zero offset section comparison, final migration stack, for: a) migration with $15\%$ error in the S-velocity model; b) residual migration with equation (6) for $\rho_p=1$, $\rho_s=1.15$ and $\gamma_0=1.92$; c) migration with the correct velocity model.

As before, we perform the initial shot profile migration with a $15\%$ positive perturbation in the S-velocity model. We perform residual migration with the RMS $\gamma_0$value at approximately 1.5 km, and $\rho_p=1$ and $\rho_s=1.15$.Residual prestack migration could not recover the image correctly at all depths. However, we got a good approximation of it. Figures 5 and 6 show our results.

 

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Figure 6 Zero offset section comparison, final migration stack, for: a) migration with $15\%$ error in the S-velocity model; b) residual migration with equation (6) for $\rho_p=1$, $\rho_s=1.15$ and $\gamma_0=1.92$; c) migration with the correct velocity model.